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math.NA2023★ 1 cited
Parameterized Wasserstein Hamiltonian Flow
Hao Wu, Shu Liu, Xiaojing Ye +1
In this work, we propose a numerical method to compute the Wasserstein Hamiltonian flow (WHF), which is a Hamiltonian system on the probability density manifold. Many well-known PD…
math.NA2023★ 1 cited
Neural Control of Parametric Solutions for High-dimensional Evolution PDEs
Nathan Gaby, Xiaojing Ye, Haomin Zhou
We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs). By employing a general nonlinear reduced-order mode…